Diffusion Barrier Performance in Real Transformer
Operation
Jonas Berntsen, Lars Arvidsson
VPdiagnose
Västerås, Sweden
Abstract - This report gives a summary of the basic theory of
gas transport in polymer membrane. It outlines important
parameters influencing the transport processes in polymer
membrane. With the theoretical background in mind, some
commercial membranes are compared and discussed with
the focus on the oxygen transmission.
Key words: sealed transformer, air bag, rubber bladder,
permeation, polymer, permeability.
Transfer of heat is also due to random molecular motions.
This analogy was recognized by Fick (1855) who adopted the
mathematical equation of heat conduction derived by Fourier
(1822). This resulted in two laws.
Fick´s first law: The rate of transfer of diffusing substance
through unit area of a section is proportional to the concentration gradient measured perpendicular to the section (1), see
Fig. 1.
J = −D
I. INTRODUCTION
In order to extend lifetime or increase temperature
endurance of transformers in operation, different methods to
prevent oxygen to enter the transformers are used.
Oxygen is the main reason for the degradation processes and
the recent increase in hot-spot (design) temperatures make
transformer sealing imperative.
The use of different materials in the diffusion barrier gives rise
to very different permeability to (primarily) oxygen. Material
thickness and structure is of utmost importance for the success
of the investment made.
Experience from recently delivered transformers seem to
suggest that manufacturers of transformers do not have an
applicable standard specification with sufficiently stringent
requirements to produce transformers with as good properties
in this aspect than was done 50 years ago.
After a summary of the diffusion theory based of the works
of Fick and Crank [1], the material properties of some
commercial barriers in transformers will be compared and
discussed with focus on the oxygen permeability.
∂c
∂x
J is the mass or molar flux, (rate of transfer per unit area of
section), c the concentration of diffusing substance, x the
space coordinate measured normal to the section, and D the
diffusion coefficient.
The negative sign arises because diffusion occurs in the direction opposite to that of increasing concentration.
Equation 1 is applicable to the diffusion in the steady state,
i.e. when the concentration does not vary with time. On the
other hand Fick´s second law describes the non-steady state
for the diffusion of a substance, which is given by the rate of
∂c
change of the substance concentration ( ) per unit area of
∂x
section:
∂c
∂ 2c
=D 2 .
∂t
∂x
II. THEORETICAL BACKGROUND
The diffusion process
Diffusion is the process by which matter is transported
from one part of a system to another as a result of random
molecular motions.
When there is a concentration gradient present in the system,
the random molecular motions result in a net transport of
molecules from high to low concentration.
(1)
A
Fig. 1. Permeation through a membrane submitted to a concentration
gradient (p1>p2)
(2)
B
Gas transport in a plane sheet (membrane)
One model to describe gas transport in a non porous barrier
is the solution diffusion model. The gas permeation is seen as
a three-stage process:
1. Adsorption and dissolution of the gas at the polymer
membrane interface.
2. Diffusion of the gas in and through the bulk polymer.
(The diffusion process in a membrane could be visualized as a
series of thermally activated jumps.)
3. Desorption of the gas into the external phase.
The transport process is characterized by an initial nonsteady state when the gas concentration profile in the
membrane is building up. During this time the process is
described by Fick´s second law. After some time, the
concentration profile within the membrane remains constant
with time (steady state). The transport through the membrane
is then described by Fick´s first law.
In the most common experimental arrangement the
membrane is initially at zero concentration and the
concentration at the face through which diffusing substance
emerges is maintained effectively at zero concentration.
The penetration of a gas in a membrane could be described by
one-dimensional diffusion in a medium bounded by two
parallel planes, e.g. the planes at x=0, x=h (the membrane’s
thickness). This means that in practice the material is so thin
that effectively all the diffusing substance enters through the
plane faces and a negligible amount through the edges.
Steady sate
In the steady state (1) is integrated to give:
J=
D(c1 − c 2 )
h
(3)
where h is the membrane’s thickness. In the case of transport
of gases and vapours, Henry’s law describes the distribution
of the penetrant between the penetrant and the polymer phase,
c = Sp
In terms of permeability, the flux (5) can be written as
J = Pe
( p1 − p 2 )
h
Non-steady state
Fig. 2. displays the plot of a permeability test. The amount
of penetrant that has passed through a membrane is plotted as
a function of time. Initially there is a transient non-steady
state, described by Fick’s second law. Finally the curve approaches the line (derived from Fick´s second law for t→∞):
Qt = (
Dc1
h2
)(t −
)
h
6D
DS ( p1 − p 2 )
h
θ = h 2 / 6D
(4)
(5)
(6)
(9)
If D is supposed to be independent of concentration it could
be determined by (9). Pe is deduced by using (7), and S
follows from (6). This procedure to determine D, Pe, and S by
analysing the stationary and non-stationary flow is referred to
as the time-lag method, introduced by Barrer 1951.
From (5) and (6) it is obvious that the flux J or the
transmission rate is dependent on the pressure difference over
the membrane and the thickness of the membrane. The
permeability coefficient, Pe , on the other hand, is normalized
for the pressure and the thickness. Thus it is convenient to use
the Pe coefficient to compare transport properties in different
membranes.
where p1 and p2 are the ambient pressures on two sides of a
film of thickness h. The product DS is called the permeability
coefficient, Pe , so that
Pe=DS
(8)
where Qt is the total amount of penetrant which has passed
through the membrane, D the diffusion coefficient, h the
thickness of the membrane and, c1 the concentration of the
penetrant at the face of high concentration. This line has an
intercept θ , time-lag, on the t-axis (Fig. 2.) given by:
where c is the concentration within the membrane. That is the
concentration of sorbed penetrant in equilibrium with the
vapour pressure p of non-sorbed penetrant. S is the solubility
coefficient.
Combination of (3) and (4) gives the permeation equation:
J=
(7)
Fig. 2. Determination of time-lag from steady state permeation [2].
C
Parameters influencing the transport properties
There are many parameters that influence the transport of
gases in a membrane. Here, the most important ones will
briefly be described. Generally these parameters influence
each other.
Temperature
The diffusion of small molecules in rubbery polymers is a
thermally activated process. At a given pressure and in a
narrow temperature interval, the transport coefficients S, D,
and Pe can be expressed by Arrhenius law:
S (T) =S0 exp (-∆HS/RT)
(10)
D(T)=D0 exp(-ED/RT)
(11)
Pe(T)=Pe0 exp(-EP/RT)
(12)
Glassy polymers (T<Tg) are non equilibrium solids that are
characterised by hard and brittle moiety with restricted chain
mobility. Rotation around the chain axis is limited and the
motion within the structure is dominated by vibration. Glassy
polymers have a specific volume larger than the specific volume of equilibrium. These characteristics lead to a more
complicated and less understood diffusion process than for
rubbery polymers.
Explanation of Tg by looking at the specific volume
If a polymer in the rubbery region is cooled, the
equilibrium specific volume will decrease linearly with the
temperature.
The pre-exponential factors represent the limit values, infinite
molecular agitation (T approaches infinity), of each transport
coefficient. Ep represents the apparent activation energy for
the permeation process and is equal to the sum of ED, the
apparent activation energy for the diffusion process, and
∆HS, the heat of solution needed for the dissolution of a penetrant mole in the polymer matrix [3]:
EP = ED + ∆HS.
(13)
Pressure
Two opposite effects may occur when the pressure on the
upstream side of a membrane is increased.
-An increased hydrostatic pressure leads to a compaction of
the polymer, thereby reducing the free volume. The diffusion
is therefore retarded
- An increased penetrant concentration which could lead to a
more plasticised polymer and a larger diffusion.
Free volume
The specific free volume VF is defined by Vrentas and
Duda [4] as:
)
)
) )
VF − V 0 = V − V (0) .
(14)
)
V is the specific volume of the equilibrium liquid structure at
)
any temperature T. V 0 is defined to be the specific volume
of the equilibrium liquid at 0 K (this quantity can be
estimated by a variety of methods [4].
Glass transition temperature, Tg
A polymer with a temperature higher than the glass
transition temperature, Tg, is in its rubbery region and
behaves like a rubber. Rubbery polymers are characterised by
segmental mobility and unsaturation. This results in smooth
and easy diffusion of small molecules. A low Tg implies large
segmental mobility and high diffusivity. In addition the increase of D with decreasing Tg is accompanied by a decrease in
concentration dependence of D.
Fig. 3. Schematic illustration of the effect
of quench rate (ri) on glass density [5]
At a certain point, there will be a deviation from the
extrapolation of the equilibrium v versus T curve applicable
in the high temperature rubbery region. This point is defined
as Tg. At slower cooling rates this point will be at lower
temperature until a minimum at “infinitely slow” cooling rate,
shown as r∞ in Fig. 2.
This inflection occurs when the potential energy for rotation
around a bond becomes of the same magnitude or greater than
the thermal energy available for motion because the main
chain is no longer able to undergo free gyration and loses its
rubber-like qualities.
Further reduction in volume can only be achieved by small
vibrations. The material then follows the less steep thermal
contraction curve characteristic of an equilibrium glass.
Fig. 3. also displays that rapidly quenched glasses (curve
r1) are less dense than slowly cooled or pressure densified
samples of the same material (curves r2 or r3). Lower density
glasses are said to have higher amounts of frozen free volume
due to the incomplete volume relaxations [5].
Degree of saturation
It has been found that the diffusivity decreases when the
degree of unsaturation is lowered by hydrogenation [6].
Saturated chains are more restricted and therefore they have
less segmental mobility than unsaturated ones.
Degree of cross linking
At low levels of cross linking, the diffusivity decreases
linearly with increasing cross linking. However higher levels
of cross-linking result in a smaller dependence on cross linking of diffusivity.
Nature of substituents
The introduction of bulky or polar groups in the polymer
chain also influences the transport properties. Rubbers
containing large numbers of substituent methyl groups have
lower diffusivities. The bulky groups reduce the mobility of
the polymer chains and the free volume available for diffusion of penetrant molecules. Studies have shown [6] that
bulky groups in the side chains have greater influence on
decreasing the diffusivity than bulky groups in the backbone.
Functional groups
The permeability of penetrants which interact weakly with
functional groups in a polymer can be expected to decrease
when the cohesive energy of the polymer increases. For
example, by increasing the polarity of the substituent group
on a vinyl polymer backbone, oxygen permeability was
reduced by almost 50000 times [6].
Plasticizer
The addition of plasticisers results in an increased segmental mobility and generally an increased penetrant
transport.
It is important to note that water could act as a plasticiser in
some materials (hydrophilic).
Molecular weight
Increased molecular weight decreases the diffusivity
significantly in glassy polymers. The number of chain ends
decrease with increasing molecular weight. The chain ends
are discontinuities that may form sites where the penetrant
could be sorbed. However, it has been found [7] that in
thermoplastic polyurethane elastomers, which are block
copolymers, composed of soft segments and hard segments,
the permeability of oxygen and carbon dioxide increased with
the chain length of the soft segments. This displays the fact
that it is not only one single parameter that influences the
transport processes but a combination of several factors.
Nature of the penetrant
The penetrant´s size and shape affect its transport rate
within the polymer matrix. An increase in penetrant size
results in a decrease of the diffusivity. The shape of the
penetrant also influences the transport. A flattened or
elongated molecule has higher diffusion coefficients than
spherical molecules of equal molecule volume.
The effects of the penetrants size and shape are more
marked in glassy than in rubbery polymers. This is because
the polymer-penetrant mixing processes are different. In
rubbery polymers, energy is required to create holes for the
penetrant molecules. Larger penetrants tend to increase the
heat of sorption resulting in increased sorption leading to an
enhanced plasticisation of the polymer chains. Thus the
smaller diffusion coefficients for larger molecules will be
compensated for by increased sorption.
Fillers
The diffusion and the transport in filled polymers depend
upon the nature of the filler. If the filler is inert and
compatible with the polymer matrix, the filler will occupy
part of the free volume resulting in a decreased permeability.
On the other hand, if the filler is incompatible with the
polymer, voids are created at the interface, leading to an
increased free volume and permeability [6].
Crystallinity
The sorption and diffusion take place only in the amorphous regions. The crystalline regions have two effects, they
increase the effective path length of diffusion and they reduce
the mobility of the polymer chains. This results in higher
activation energy of diffusion.
Orientation
Uniaxially drawing of the polymer, changes its morphology
and could both increase and decrease the transport
parameters.
Diffusion in polymer blends
The transport through a blend depends on its composition,
miscibility and phase morphology. In homogenous blends the
diffusion is influenced by the interaction between the
component polymers, while for heterogeneous blends, the
interfacial phenomena and the rubbery or glassy nature of the
phases are important. Most polymer blends are heterogeneous.
III. CHOOSING MATERIAL IN POWER
TRANSFORMER SEALING BAGS
To obtain a membrane with a low oxygen diffusion rate it is
important to obtain a material that possesses both high barrier
properties and high flexibility to avoid material rupture.
It is difficult to find a single material that combines both of
these properties. High flexibility generally means high permeability because of large segmental motions. Similarly a high
barrier often means a rigid material. Therefore one is directed
to blends or laminates that combine the required properties.
IV.
THE REALITY
In the commercial application people responsible for
ordering the rubber bags seem to have forgotten WHY they
are ordered. This is also the case with the suppliers.
Attempts to obtain gas diffusion data from various
suppliers have failed because the data are not available and
maybe never have been available. This means that materials
are chosen based on cost and flexibility rather than
performance and cost which is more to be expected in
technical applications.
As a consequence today's rubber bag sealed transformers
have very low sealing tightness, especially in comparison
TABLE I
NITROGEN ANNUAL INCREASE
Sealing quality
Annual N2 increase
Years to N2-saturation
Good
1 000 ppm
> 50
Acceptable
2-3 000 ppm
20- 40
Unacceptable
> 5 000 ppm
10
Today’s best
5 000 ppm
10
Today’s worst
1 000 000 ppm
2 weeks
with sealed transformers from the 1950´s and 1960´s. In fact
some of the very recent transformers tested during commissioning/warranty period has made it necessary to investigate
whether they actually had a rubber bag.
It is easy to measure the tightness against atmospheric
gases as nitrogen, the most abundant of atmospheric gases, is
inert. Oxygen is not suited for this as the oxygen level in a
faulty and sealed transformer can become very low as oxygen
is consumed due to the heat generated by the fault.
TABLE I displays the annual increase of nitrogen for some
transformers in different condition. “Good” are measured data
from 50 years old transformers from Iceland. Iceland's
volcanic foundation and its H2S-rich atmosphere convinced
the Icelandic engineers to choose sealed designs to avoid
sulphur corrosion. On the same time they received an extra
bonus of extreme life times as oxygen was also excluded from
the transformers.
Today's best and worst are measured very recently and
range from 20 MVA to HVDC transformers of >500 MVA.
V.
DISCUSSION AND SUGGESTIONS
The decline in chemical performance (=life time
parameters) need to be addressed by the purchasing side by
specifications that include the life time aspects such as rubber
bag seals (extending life time by not allowing oxygen to enter
the insulation system).
The development towards lower and lower quality rubber
bag sealing materials can be handled when ordering the
transformer by simply state the requested maximum annual
in-flow of air gases and state that it should be measured by
monitoring the N2-content rate of change according to a standardized test method. Because of the influence of several
parameters on the permeability, the method should specify the
pre conditioning of the membrane. This means that the
membrane is kept at constant conditions, temperature,
pressure, (and relative humidity. The relative humidity should
not be an important parameter, because the material should be
chosen not be sensitive to humidity.), prior to measuring. The
test should also be run under these constant conditions and the
results should be reported in permeability units, which make
it possible to compare different materials. Then it will be up
to the transformer designer to ensure this is done. By this
method any other leaky points e.g. at bushings, circulation
pumps etc. will also have to be addressed by the designer and
better sealing would be chosen there too.
It is essential to understand that carefully monitoring air
gases levels in insulating oil systems require very stringent
sampling procedures, sample transportation methods and
analytical techniques. Syringes and Head-Space laboratory
analytical methods have proven to be extremely vulnerable to
contamination of the sample by atmospheric gases rendering
the analytical results always to come out to high. Thus that
methodology is not suited for diagnosing diffusion of
atmospheric gases into the insulation system of a transformer.
REFERENCES
[1] Crank, J. The Mathematics of diffusion. Oxford University Press.
1975.
[2] Chih-Yi Chen, J. Evaluation of Polymeric Membranes for Gas
Separation Processes: Poly (ether-b-amide) (PEBAX2533) Block
Copolymer. Dissertation. 2002. The University of Waterloo, Ontario,
Canada.
[3] Klopffer, M.H.; Flaconnèche, B. Transport Properties of Gases in
Polymers: Bibliographic Review. Oil & gas Science and Technology- Rev.
IFP. 2001, 56(3): 223-244.
[4] Vrentas, J.S.; Duda, J.L. Diffusion in Polymer-Solvent Systems. I.
Reexamination of the Free-Volume Theory. J. Polym Sci., Part B: Polym
Phys. 1977, 15, 403-416.
[5] Koros, W.J. Sorption and Transport of Gases in Glassy Polymers;
Dissertation. 1977. The University of Texas at Austin.
[6] George, S.C.; Thomas, S. Transport Phenomena through Polymeric
Systems. Prog. Polym. Sci. 2001, 26, 985-1017.
[7] Matsunaga, K. Gas Permeability of Thermoplastic Polyurethane
Elastomers. Polymer Journal, 2005, 37(6), 413-417.
About the authors:
Jonas Berntsen, born in 1971. He graduated from
Chalmers University of Technology, Göteborg, Sweden,
2001. M.Sc. in Chemical Engineering.
Mr Berntsen has been working in research
projects on diffusion in biopolymer membranes.
He has been employed at SIK, Institute of
food science and biotechnology, Göteborg,
Sweden and at University Federico II, Naples,
Italy.
Lars Arvidsson, born in 1954. He graduated from the University of Technology in Lund Sweden in 1979. M.Sc. in
Chemical Process Engineering.
Mr Arvidsson has been employed with
ASEA, ABB and Vattenfall in Sweden.
He is the founder, owner and General
Manager of VPdiagnose/ Västerås PetroleumKemi AB (1994).